1. Field of the Invention
The present invention relates to an apparatus and a method for determining a mark position on a wafer, and more particularly, to an apparatus and a method for determining a mark position used in delineating a plurality of registered patterns using a beam such as an electron beam in lithography of semiconductor device fabrication.
2. Description of the Background Art
In lithography of semiconductor device fabrication, a pattern generation apparatus is conventionally known. This apparatus prestores a desired pattern in a storage device, and delineates the stored pattern by electron beam exposure on a silicon substrate, which is coated with resist and mounted on a stage. In lithography of semiconductor device fabrication, 10 to 30 patterns such as a pattern for forming an oxide film and a pattern for forming a gate electrode of a transistor must be registered. In order to register the patterns, the position of an alignment mark which is a groove formed on the silicon substrate must be determined. The position of a pattern formed in the previous step is determined by the position of the alignment mark. In the recent development of LSI whose patterns get smaller, the patterns must be registered with high accuracy of 0.1 .mu.m or less. Therefore, extremely high accuracy is required for detection of the alignment mark.
Information on an electron signal reflected from the silicon substrate irradiated with an electron beam is different between in a portion including the alignment mark and in a portion not including the alignment mark. In determination of the position of the alignment mark, this difference is used. More specifically, the vicinity of the alignment mark on the silicon substrate is scanned by the electron beam and the position of the mark is determined based on a reflected electron signal detected by scanning.
FIG. 13 shows a specific structure of a conventional apparatus for determination of an alignment mark position.
Referring to FIG. 13, a silicon substrate 126 having resist 125 is irradiated with an electron beam 103 emitted from an electron gun (not shown). Information on an electron signal reflected from silicon substrate 126 irradiated with electron beam 103 is detected by a reflected signal detector 106. Electron beam 103 is deflected by a beam deflector 104 constituted of opposing electrodes, and scans the vicinity of an alignment mark 111 of silicon substrate 126 depending on the degree of deflection. The intensity of the reflected electron signal indicates a curve shown in FIG. 14. In this figure, the distance for which the beam moves on a line including the alignment mark on the silicon substrate by scanning is plotted along the abscissa, and the intensity of the electron signal reflected from the silicon substrate is plotted along the ordinate. This curve is generally called a reflected signal waveform. When the line including the alignment mark is scanned as shown in FIG. 14, ideal reflected signal waveform 113 is in symmetry. The level of waveform 113 is high in a portion not including the alignment mark and low in a portion including the alignment mark. By finding the center position of the symmetrical reflected signal waveform, the center position of the alignment mark is determined. The position of the silicon substrate is determined by an output from a laser interferometer, and the position at which the silicon substrate is irradiated with the electron beam is determined by a voltage applied to beam deflector 104. Since the alignment mark is formed by a groove having a depth of approximately 0.1 to 1.0 .mu.m as shown in FIG. 13, resist 125 becomes thick in the portion of the groove, and the distance to the substrate from which the electron is reflected becomes long. Therefore, electrons lose energy in resist 125 in their path. This is the reason why the level of the reflected signal waveform in the portion including the alignment mark becomes low.
A "threshold method" and an "autocorrelation method" are employed as a method for calculating the center position of the alignment mark based on the reflected signal waveform shown in FIG. 14. These methods will be described.
FIG. 15 shows the reflected signal waveform converted into an electric signal by detector 106, and FIG. 16 is a diagram for describing the signal processing of the reflected signal waveform by the threshold method.
Referring to FIG. 15, the intensity of a signal 114 reflected from the portion including the alignment mark (groove) tends to be smaller than that of a signal 127 reflected from the region not including the alignment mark (hereinafter referred to as a "base line"). In the threshold method, a threshold level 115 is set at a height of 30 to 70%, when the minimum value of the signal reflected from the portion including the alignment mark is 0% and the base line is 100% as shown in FIG. 16. Then, crossing points 128a and 128b between threshold level 115 and reflected signal waveform 113 are calculated, and a center position 117 between two crossing points 128a and 128b is determined as the center position of the alignment mark.
On the other hand, in the autocorrelation method, the reflected signal waveform shown in FIG. 15 is digitally sampled and input to the apparatus. Here, assume that the digitally sampled waveform is D(X). The waveform D(X) is substituted in an autocorrelation function Z(X) shown by the following expression (1). The waveform indicated by Z(X) calculated according to the expression (1) is called an autocorrelation signal. ##EQU1##
Note that in the expression (1), a variable W is arbitrarily set as a width a little larger than that of the alignment mark (groove). By the processing of the reflected signal waveform shown in FIG. 15 with the autocorrelation method according to the expression (1), the autocorrelation signal shown in FIG. 17 is calculated. The autocorrelation signal indicates a so-called centroid of the reflected signal waveform, peak position 119 of which is to be determined as the center position of the alignment mark.
However, in the above described apparatus for determining the alignment mark position, the center position of the alignment mark cannot be always determined accurately because of the following reason. As shown in FIG. 19A, in the actual lithography, a thin film 120 of atoms of platinum, tungsten or the like is sometimes formed between silicon substrate 126 and resist 125. Since the atoms of platinum or tungsten of thin film 120 have a large atomic number and a large density, the reflection coefficient of an electron is extremely large. Therefore, when the thickness of thin film 120 is different in the alignment mark portion as shown in FIG. 19A, the reflected signal waveform is in asymmetry as shown in FIG. 19B. More specifically, the intensity of the signal reflected from the thick portion of thin film 120 is relatively large, while that of the signal reflected from the thin portion of thin film 120 is relatively small. Therefore, center position 121 of the alignment mark calculated from reflected signal waveform 113 by the threshold method tends to shift towards the side of thin film 120 having a small thickness as shown in FIG. 19B. Similarly, also when the peak position is calculated by the autocorrelation method, the peak position shifts towards the side of thin film 120 having a small thickness as shown in FIG. 19C.
If thin film 120 is formed uniformly in symmetry in the alignment mark portion, such shift in the mark center position does not occur. However, as shown in FIG. 18, the thin film is currently formed with a spattering method. In the spattering method, a voltage is applied between silicon substrate 126 and a target 205, and the material of target 205 is deposited on silicon substrate 126 as a thin film. Therefore, thin film 120 at alignment mark 111 having a three-dimensional shape varies in thickness depending on its positional relationship with target 205. In an example shown in FIG. 18, the left portion of alignment mark 111 in the figure has a large thickness since the film is directly exposed to target 205, while the right portion of alignment mark 111 has a small thickness since this portion is shadowed by silicon substrate 126.